102 LearnersLast updated on May 26th, 2025
Factors of 1065
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing items equally, arranging things, etc. In this topic, we will learn about the factors of 1065, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1065?
The numbers that divide 1065 evenly are known as factors of 1065.
A factor of 1065 is a number that divides the number without a remainder.
The factors of 1065 are 1, 3, 5, 15, 71, 213, 355, and 1065.
Negative factors of 1065: -1, -3, -5, -15, -71, -213, -355, and -1065.
Prime factors of 1065: 3, 5, and 71.
Prime factorization of 1065: 3 × 5 × 71.
The sum of factors of 1065: 1 + 3 + 5 + 15 + 71 + 213 + 355 + 1065 = 1728
How to Find Factors of 1065?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using division method
- Prime factors and Prime factorization
Finding Factors Using Multiplication
To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 1065. Identifying the numbers which are multiplied to get the number 1065 is the multiplication method.
Step 1: Multiply 1065 by 1, 1065 × 1 = 1065.
Step 2: Check for other numbers that give 1065 after multiplying
3 × 355 = 1065
5 × 213 = 1065
15 × 71 = 1065
Therefore, the positive factor pairs of 1065 are: (1, 1065), (3, 355), (5, 213), (15, 71).
All these factor pair result in 1065.
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with the whole numbers until the remainder becomes zero and listing out the numbers which result as whole numbers as factors. Factors can be calculated by following a simple division method -
Step 1: Divide 1065 by 1, 1065 ÷ 1 = 1065.
Step 2: Continue dividing 1065 by the numbers until the remainder becomes 0.
1065 ÷ 1 = 1065
1065 ÷ 3 = 355
1065 ÷ 5 = 213
1065 ÷ 15 = 71
Therefore, the factors of 1065 are: 1, 3, 5, 15, 71, 213, 355, 1065.
Prime Factors and Prime Factorization
The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:
- Using prime factorization
- Using factor tree
Using Prime Factorization: In this process, prime factors of 1065 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1065 ÷ 3 = 355
355 ÷ 5 = 71
71 ÷ 71 = 1
The prime factors of 1065 are 3, 5, and 71.
The prime factorization of 1065 is: 3 × 5 × 71.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 1065 is divided by 3 to get 355.
Step 2: Now divide 355 by 5 to get 71.
Step 3: 71 is a prime number and cannot be divided further. So, the prime factorization of 1065 is: 3 × 5 × 71.
Factor Pairs Two numbers that are multiplied to give a specific number are called factor pairs.
Both positive and negative factors constitute factor pairs.
Positive factor pairs of 1065: (1, 1065), (3, 355), (5, 213), (15, 71).
Negative factor pairs of 1065: (-1, -1065), (-3, -355), (-5, -213), (-15, -71).
Common Mistakes and How to Avoid Them in Factors of 1065
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
Mistake 1
Forgetting the number itself and 1 is a factor
Children might forget to add the given number itself and 1 as a factor. The number itself and 1 are the factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 1065, 1 and 1065 are also factors.
Factors of 1065 Examples
Problem 1
There are 5 friends and 1065 candies. How will they divide it equally?
They will get 213 candies each.
Explanation
To divide the candies equally, we need to divide the total candies with the number of friends.
1065/5 = 213
Problem 2
A rectangular field has a length of 71 meters and a total area of 1065 square meters. Find the width.
15 meters.
Explanation
To find the width of the field, we use the formula,
Area = length × width
1065 = 71 × width
To find the value of width, we need to shift 71 to the left side.
1065/71 = width
Width = 15.
Problem 3
There are 3 trucks and 1065 boxes. How many boxes will be in each truck?
Each truck will have 355 boxes.
Explanation
To find the boxes in each truck, divide the total boxes with the trucks.
1065/3 = 355
Problem 4
In a tournament, there are 1065 players, and 71 teams. How many players are there in each team?
There are 15 players in each team.
Explanation
Dividing the players with the total teams, we will get the number of players in each team.
1065/71 = 15
Problem 5
1065 pages need to be bound into 5 books. How many pages will go in each book?
Each book will have 213 pages.
Explanation
Divide total pages with books.
1065/5 = 213
FAQs on Factors of 1065
1.What are the factors of 1065?
2.Mention the prime factors of 1065.
3.Is 1065 a multiple of 5?
4.Mention the factor pairs of 1065?
5.What is the square of 1065?
6.How can children in Singapore use numbers in everyday life to understand Factors of 1065?
7.What are some fun ways kids in Singapore can practice Factors of 1065 with numbers?
8.What role do numbers and Factors of 1065 play in helping children in Singapore develop problem-solving skills?
9.How can families in Singapore create number-rich environments to improve Factors of 1065 skills?
Important Glossaries for Factors of 1065
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1065 are 1, 3, 5, 15, 71, 213, 355, and 1065.
- Prime factors: The factors which are prime numbers. For example, 3, 5, and 71 are prime factors of 1065.
- Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of 1065 are (1, 1065), (3, 355), etc.
- Prime factorization: The process of expressing a number as a product of its prime factors. For instance, the prime factorization of 1065 is 3 × 5 × 71.
- Division method: A method to find factors by dividing the number by whole numbers until a remainder of zero is achieved, listing those divisors as factors.
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About BrightChamps in Singapore
Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
